Which recursive formula can be used to define this sequence for n > 1? 5, 19, 33, 47, 61, 75, ... Choices: (A)a = a + 14 (B)a = a + a - 14 (C)a = 14a (D)a = 19/5a

Determine Sequence Type: Analyze the sequence to determine if it is arithmetic or geometric. The sequence is 5, 19, 33, 47, 61, 75, ... To determine if it is arithmetic, we check if the difference between consecutive terms is constant. 19 - 5 = 14, 33 - 19 = 14, 47 - 33 = 14, and so on. Since the difference is constant, the sequence is arithmetic.Find Common Difference: Find the common difference, d, for the arithmetic sequence. Using two consecutive terms, 19 and 5, we calculate the common difference. d = 19 - 5 = 14 The common difference (d) is 14.Identify Recursive Formula: Identify the recursive formula for the given arithmetic sequence. Since the sequence is arithmetic with a common difference of 14, the recursive formula will be of the form: a_n = a_(n-1) + d Substituting the common difference, we get: a_n = a_(n-1) + 14

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $5, 19, 33, 47, 61, 75, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + 14$ $\newline$ (B) $a_n = a_{n-1} + a_{n-1} - 14$ $\newline$ (C) $a_n = 14a_{n-1}$ $\newline$ (D) $a_n = \frac{19}{5}a_{n-1}$

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Math Problems

Algebra 1

Write a formula for a recursive sequence

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Q. Which recursive formula can be used to define this sequence for

n > 1

\newline

5, 19, 33, 47, 61, 75, \ldots

\newline

Choices:

\newline

(A)

a_n = a_{n-1} + 14

\newline

(B)

a_n = a_{n-1} + a_{n-1} - 14

\newline

(C)

a_n = 14a_{n-1}

\newline

(D)

a_n = \frac{19}{5}a_{n-1}

Determine Sequence Type: Analyze the sequence to determine if it is arithmetic or geometric. $\newline$ The sequence is $5, 19, 33, 47, 61, 75, \ldots$ $\newline$ To determine if it is arithmetic, we check if the difference between consecutive terms is constant. $\newline$ $19 - 5 = 14$ , $33 - 19 = 14$ , $47 - 33 = 14$ , and so on. $\newline$ Since the difference is constant, the sequence is arithmetic.
Find Common Difference: Find the common difference, $d$ , for the arithmetic sequence. $\newline$ Using two consecutive terms, $19$ and $5$ , we calculate the common difference. $\newline$ $d = 19 - 5 = 14$ $\newline$ The common difference ( $d$ ) is $14$ .
Identify Recursive Formula: Identify the recursive formula for the given arithmetic sequence. $\newline$ Since the sequence is arithmetic with a common difference of $14$ , the recursive formula will be of the form: $\newline$ $a_n = a_{n-1} + d$ $\newline$ Substituting the common difference, we get: $\newline$ $a_n = a_{n-1} + 14$